Adding Integers - Free Educational videos for Students in K-12

Adding Integers - By Anywhere Math

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00:0-1	I played a par three course this summer and got
00:02	my first hole in one out of the nine holes
00:05	. I got seven pars , one bogey and one
00:09	eagle . The hole in one . What was my
00:11	total score after nine holes ? Welcome to anywhere .
00:32	Math . I'm Jeff , Jacobson . And today we're
00:34	gonna talk about adding into juice . Okay , let's
00:38	talk about that golf score . Now , if you
00:39	don't know much about golf , this could be pretty
00:42	difficult . Uh , so let's talk a little bit
00:44	about some of those keywords first . Uh , I
00:47	played nine holes , right ? And it was a
00:53	par three course . Yeah , yeah . Okay .
01:02	Now what that means is every hole was a par
01:06	three and what that means is you're expected to take
01:11	three shots to get the ball in the hole .
01:13	Um if you take more than three then you're over
01:17	part . If you take less than three , that's
01:20	good because that means you're getting it in less than
01:24	you expected to , which is good , you would
01:26	be under part . So a par equals you're even
01:35	, that means you're not above part , you're not
01:38	below part , you're exactly what you were supposed to
01:40	be . Uh And we can represent that with an
01:43	integer of zero . A bogey means you were one
01:52	stroke or one hit over par . So one over
01:58	And we can represent that with a positive one or
02:02	a plus one . Okay . In order uh if
02:07	you were below par , so one below is called
02:11	a birdie , that's one . Uh Instead of below
02:17	engulf they say under . Also I'll say you're one
02:22	under par Which we would represent as a -1 .
02:28	Uh If you were to under that's called an eagle
02:35	. Uh And then in a par three that would
02:38	be a hole in 12 under par , two under
02:45	would be a negative too . If you remember on
02:48	my round I had seven pars . Um one hole
02:56	in one and one bogey . Okay so the question
03:08	is , what's my overall score relative to par ?
03:12	Well seven pars apart as even its has a value
03:16	of zero . So seven of them would still just
03:20	be zero plus hole in one On a par three
03:26	course . That means I got it in one shot
03:29	which is was pretty exciting . Let me tell you
03:31	. Uh And that would be on a par three
03:34	. That would mean I got an eagle technically .
03:37	So that's to wonder . So I'm gonna add A
03:42	-2 . Okay then I had one bogey which is
03:46	one over . So I'm also going to add a
03:49	plus . I'll just say I don't need to put
03:52	in parentheses plus one . So my overall score for
03:57	those nine holes zero plus negative two is negative two
04:01	Plus one . That's a positive one , gives me
04:05	-1 . Can't that means I was one under par
04:11	for nine holes , Which is not too bad .
04:14	All right . Today we're adding integers . Remember ,
04:17	integers are just it could either be positive or negative
04:20	whole numbers and also include 00 is an energy .
04:23	Don't forget that . Uh So our first example ,
04:26	we are adding integers with the same sign , introduce
04:30	that have the same sign . So either both of
04:32	them are positive or both of them are negative .
04:34	So our first example negative two plus negative seven .
04:38	Uh There's a couple ways that we can think about
04:42	that . Um First you can think of it as
04:45	well . I have two negatives negative negative . Um
04:51	Maybe I'll put a little circle so it's easy .
04:54	Plus seven more negatives . So one , 23 for
05:03	56 seven . Okay , well , if I've got
05:09	two negatives plus seven more negatives , how many negatives
05:12	do I have ? uh and two plus 7 is
05:16	nine . I've got nine negatives 123456789 . So my
05:26	answer is just no you're not okay , that's one
05:31	way to think about it . Uh But obviously that
05:34	can kind of take a long time if you're going
05:36	to draw that out . Um But conceptually hopefully that
05:39	helps another way we can think of it as uh
05:43	if we use a number line . So if I
05:46	draw a number line I'm always gonna start at zero
05:52	when I'm when I'm simplifying expressions and things like this
05:55	, I'm gonna start at zero . So here's zero
05:59	From there I go to negative 2 1st So here's
06:04	negative one -2 . So I started zero And I
06:10	moved to negative two then from negative to I'm going
06:13	to add -7 So I'm adding that on to the
06:16	end of it . Uh so I'm going negative seven
06:20	more . So that would be -3 . You know
06:24	for 85 , 8-7 and I need a little bit
06:30	more room -8 and -9 . So I'm going seven
06:38	more right 1234567 and I am at -9 same thing
06:49	. Right ? So this was the negative to that
06:52	was the -7 . So those are a couple ways
06:55	uh that you can kind of think conceptually about what's
06:59	going on when we're adding two images that have the
07:02	same sign . Uh But hopefully you'll start to realize
07:06	all I really need to do is add the absolute
07:11	value . So basically just add the digit and then
07:15	if it was if they were both negative , your
07:17	answer is going to be negative . If they were
07:19	both positive you're asking is going to be positive .
07:22	Here's something try on your own . Okay . Before
07:29	we get to the next example we gotta figure out
07:32	something . So what is six plus a negative six
07:36	? Um Some of you might already know but let's
07:39	let's kind of work through this to really uh kind
07:41	of get a better understanding . Uh So if we
07:45	if we did if we saw this problem the same
07:47	as kind of what we did on the first example
07:51	, I've got six positives notice these aren't the same
07:54	sign , we've got a positive and a negative .
07:56	So I could represent those six positives . 123456 with
08:04	six plus is a plus for positive . Then I'm
08:07	adding six negatives . So I'm gonna write 123456 Okay
08:14	those negatives . Well what's going to happen with this
08:18	positive in this negative is that they're gonna cancel each
08:21	other out ? Okay Just like uh yeah , they
08:26	become zero or cancel each other out . So I'm
08:28	just gonna kind of cross all those off if they
08:32	all cancel each other out , what am I left
08:34	with ? And hopefully you can realize you're left with
08:37	zero . Okay , So six plus negative six zero
08:42	. Another way that we can think of it as
08:44	with a number line again . All right . If
08:48	I start at zero , just like always And I
08:53	go up to 6 1st . That's the first number
08:55	I'm starting with . Mhm . Yeah . So 1
09:01	, 2 , 3 , 4 , 5 and six
09:07	. And then from there I had a negative six
09:09	and negative . We're going to the left . So
09:12	then these are different color . I'm going -6 .
09:18	So I'm going to the left , where am I
09:21	back at zero again ? Which is again why six
09:25	plus in a year six equals zero . Now ,
09:29	this has a name . Okay . This is called
09:32	the additive inverse property . Okay . Yeah . Yeah
09:48	. And the additive inverse property . You can see
09:50	additive , which means we're adding integers inverse . Um
09:56	basically you can think of that as the opposite .
09:58	So additive inverse property just means that the sum of
10:06	an integer it and its inverse . And again in
10:17	verse you can think of it as opposite , Right
10:23	? The opposite of six is negative six Or the
10:26	opposite of -6 is six . Those are opposites The
10:30	some right , we're adding that's why we say some
10:33	the some of an integer and its inverse or opposite
10:38	is zero . Okay , so 12 plus negative 12
10:44	0 negative three plus +30 Whenever you're adding opposites or
10:50	inverse , you're going to get a sum of zero
10:53	. That's the additive inverse property . Let's try another
10:56	example . Here's example to now we're adding integers with
11:01	different signs . No longer do we have two images
11:05	that are either both positive and negative ? Now we've
11:08	got one of each so negative three plus seven .
11:12	Again , we can still use the same strategy .
11:15	We can solve this with We've got -3 . That
11:19	could be like negative three negatives plus uh seven positives
11:28	1234567 . And you can see that this negative and
11:36	this positive would cancel each other out this one same
11:40	thing and same thing . And look what we have
11:44	left . We have four positives left , which means
11:47	negative three plus seven is four . Now we could
11:53	also solve this with A number line . Okay ,
12:00	start at zero . Yeah , I'm going to negative
12:04	3 1st . So that's maybe native groups negative one
12:13	, negative two , negative three . Uh And then
12:18	I'm going Positive 7-plus positive seven . So going positive
12:23	, I'm going to the right . Mhm . So
12:29	that's three that I'm going to go four more ,
12:31	so there's 123 four . Okay so this was the
12:40	Native three and this was Plus seven . So again
12:47	where did I end up positive four . Okay so
12:52	again those strategies can still work . Um Let's look
12:55	at another one . Okay . Part B . 37
13:00	plus negative 56 . Now we could do the same
13:07	strategy . But to be honest , I don't want
13:11	to write out 37 plus is And 56 negative signs
13:16	. And then cross things out . I don't want
13:18	to really do a number line because that same thing
13:21	would take forever . Um So there's gotta be another
13:24	way that we could do this and there is when
13:28	you are adding integers that have different signs , all
13:33	you have to do is take the absolute value of
13:37	the numbers and we just we know what absolute value
13:39	is . We just did that in the last video
13:42	uh and subtract them subtract the greater Absolute value from
13:46	the less absolute value . Okay so absolute value of
13:49	37 is 37 Absolute value of negative . 56 is
13:54	56 . So 56 is greater . So I'm gonna
13:57	mm Put that up top and I'm gonna subtract 37
14:02	from it . Mhm . Okay so I am 19
14:06	. Now this is the most important part . After
14:10	you get your difference here you have to look back
14:13	at your original problem and whichever number uh whichever had
14:20	the greater absolute value . That's the sign that you're
14:23	going to use . So which one had the greater
14:27	absolute value . The absolute value of this was 37
14:30	. The absolute value of -56 is 56 which means
14:34	this has the greater absolute value , It's negative ,
14:38	which means my answer is negative . So that's -19
14:46	. And if you think logically , That should make
14:49	sense . Right ? If you wanna , if you
14:51	wanna do all those pluses and minuses , you'd have
14:54	37 plus marks , You have 56 negatives . So
14:59	once you cancel out all of these , you're still
15:02	going to have more negatives left over . Which is
15:05	why your answer is negative or same thing . If
15:07	you think logically with the number line , uh it
15:10	would make sense that way . Alright , this last
15:12	1 -12 plus 12 . Hopefully you notice that these
15:17	are opposites right there in verses of each other .
15:22	Uh and if you remember the additive inverse property ,
15:27	anytime you're adding opposites are adding in verses , Your
15:31	son is going to be zero . So native 12
15:34	plus 12 is zero . Thanks for watching . And
15:43	if you like this video , please subscribe

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